My Background

Analyzing Baseball Data with R

• 3rd edition (with Max Marchi and Ben Baumer) available soon

• Online version available at https://beanumber.github.io/abdwr3e/

• Book blog at https://baseballwithr.wordpress.com/

• 60 posts on aspects of home run hitting

Historical View of Home Runs

• Baseball Reference provides the average number of Home Runs, Hits, Runs for each team each game during all seasons of Major League Baseball (1871 through 2023)

• Home Run hitting has gone through many changes in MLB History

Avg HR Hit Per Team Per Game

Seasons of Famous HR Hitters

Some Famous HR Seasons

• Frank (Home Run) Baker (1914)
• Babe Ruth (1927)
• Roger Maris (1961)
• Mark McGwire (1998)
• Barry Bonds (2001)

Home Run Baker

Babe Ruth

Roger Maris

Mark McGwire

Barry Bonds

HR Totals in the Statcast Era

A Plate Appearance

Three Basic Outcomes:

• Strikeout
• Walk
• Ball put into play

How have the rates of these three outcomes changed over the last 50 years of baseball?

History of Strikeout Rates

History of Walk Rates

History of In-Play Rates

History of Rates

• SO Rates have been steadily increasing

• In-Play Rates have been decreasing

• Pattern of Walk Rates are less clear, show up and down movement

In-Play Rates

• Define the home run rate as the fraction of \(HR\) among all batted balls (\(AB - SO\))\[ HR \, Rate = \frac{HR}{AB - SO} \]

• Look at history of \(HR\) rates

History of HR Rates

MLB Committee

• Fall of 2017 a committee was charged by Major League Baseball to identify the potential causes of the increase in the rate at which home runs were hit in 2015, 2016, and 2017.

• Report was released in May 2018.

Possible Reasons for Increase in HRs

The batters?

• Changes in characteristics of batted balls
• Launch angle, exit velocity, and spray angle

The pitchers?

• Changes in types of pitches
• Pitch location

Possible Reasons for Increase in HRs

The ball?

• Changes in how the ball is made?
• Seam height, core?
• Drag coefficient?

Possible Reasons for Increase in HRs

Game conditions?

• Ballpark effect
• Weather
• Cold vs. hot temperatures

Process of Hitting a Ball

• IN-PLAY: Have to put the ball in play

• HIT IT RIGHT: The batted ball needs to have the “right” launch angle and exit velocity

• REACH THE SEATS: Given the exit velocity and launch angle, needs to have sufficient distance and height to clear the fence (the carry of ball)

Committe’s Findings (2015-2017 Data)

• Found modest changes in launch angle and exit velocity among batters
• Focused on RED zone – launch angle in (15, 40) degrees, launch speed between 90 and 115 mpg
• The RED zone balls are showing more carry – they travel further

Committee’s Findings

• Increase in home runs is due to better carry (less drag) for given launch conditions
• Likely due to the aerodynamic properties of the baseball
• Didn’t appear to be a property of the manufactured baseballs
• Recommend that MLB monitor the climate environment of the baseballs

End of 2023 Season

• Nine seasons of Statcast data (2015 - 2023) are available
• Have launch speed and launch angle measurements for all seasons
• Take a broader perspective on home run hitting

Empirical Approach

• Look at region of launch angle and exit velocity where most of home runs are hit
• Look at rate of batted balls in this region – how does it vary by season?
• Look at rate of home runs for balls hit in this region – how does it vary season?

Launch Vars Where Most HR are Hit (RED Zone)

Balls in Play Rate

• Interested in rate of “home run likely” (RED Zone) batted balls \[ BIP \, Rate = \frac{HR \, Likely}{BIP} \]
• Are batters changing their approach?
• Players getting stronger?

Rate of Balls Hit in RED Zone

Rate of Balls Hit in RED Zone

• See a general increase in “home run likely” rates over Statcast period
• Players appear to be changing their hitting approach or they are getting stronger

Home Run Rate in RED Zone

• What is the chance of a home run given good values of launch angle and exit velocity? \[ HR \, Rate = \frac{HR} {HR \,Likely} \]
• Characteristic of the baseball
• Changes in drag coefficient over seasons?

Home Run Rate in RED Zone

Home Run Rate in RED Zone

• General increase from 2015 to 2017
• Big dip in 2018, followed by big increase in 2019
• General decrease from 2019 to 2023
• These “ball effects” are large

Aaron Judge

Aaron Judge in 2022

• Hit 62 home runs during a season when the ball was relatively dead

• Raises the question: How many home runs would Judge hit during a different season during Statcast era?

Methodology

• Suppose the different season is 2019.

• Fit a “2019 ball model” that predicts the probability of a HR in 2019 given values of the launch angle and exit velocity.

• Collect the launch variables for Judge for all balls put into play. For each BIP, predict P(HR) using 2019 ball model.

• Sum the probabilities – predict the season HR.

Generalized Additive Model

• \(logit(P(HR)) = s(LA, LS)\)

• \(s()\) is a smooth function of the launch angle (LA) and the launch speed (LS)

• Generalization of the linear regression model \(y = X \beta + \epsilon\)

Predict

• For each Judge’s BIP in 2022, predict the probability of HR from the launch variables using the 2019 ball model.

• Sum the probabilities – predict total HR count

• Can get a 90% prediction interval

Results

• If Judge was hitting using a 2019 ball, predict he would hit 75 home runs

• A 90% prediction interval would be (69, 81)

Repeat this method for other Statcast seasons

• Use GAM model to predict prob(HR) from the launch angle and exit velocity for one season

• Use this ball model to predict HR probability using 2022 launch variables

• Sum prediction probabilities

Results

Takeaway

• Judge only hit 62 home runs in 2022

• But if he was playing during a different Statcast season where the ball was more alive (more carry), we’d predict his 2022 count to be in the 70’s

• So Judge’s home run achievement is understated

• Due to this ball bias, we don’t appreciate magnitude of Judge’s accomplishment

Concluding Comments

• Many factors influence home run hitting.

• Two important factors are the hitters (values of launch variables) and the ball (carry or drag coefficient).

• It is helpful to monitor the Balls-in-Play and Home Run rates to see the effects due to the hitters and the ball.

Concluding Comments (Continued)

• Batters are stronger and changing their hitting approach, leading to higher rates of “HR friendly” balls in play.

• The composition of the ball has gone through dramatic changes during the Statcast era.

• Currently the ball is relatively dead compared to previous seasons.